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The U.S. State Department rolled out travel and visa restrictions on Venezuelan officials accused of human rights violations. But South Florida lawmakers say the sanctions don’t go far enough.

Even as the U.S. State Department slapped Venezuelan officials with travel restrictions and revoked their visas over human rights violations, lawmakers Wednesday asked for steeper penalties, including the freezing of assets in the United States.

The sanctions were imposed in response to a government crackdown on protests earlier this year that left hundreds injured and 42 dead on both sides of the political dispute. As the administration has jailed opposition leaders and protesters, rights groups have raised flags about torture and the excessive use of force.

“With this step we underscore our commitment to holding accountable individuals who commit human rights abuses,” Marie Harf, the State Department’s deputy spokeswoman, said in a statement. “While we will not publicly identify these individuals because of visa record confidentiality, our message is clear: those who commit such abuses will not be welcome in the United States.”

Later, Harf said ministers, presidential advisers, judicial officials and law enforcement and military personnel were among those targeted.

Foreign Minister Elías Jaua said the sanctions were designed to undermine what he sees as Venezuela’s growing regional influence.

“It’s a desperate scream from those who know the world is changing and have no way to react to this new reality but through aggression and imperial arrogance,” he said in a broadcast statement.

The sanctions mark a new low for the two countries, which haven’t had ambassadors since 2010. But the travel ban may be just the beginning.

On Wednesday, Sen. Marco Rubio, a Florida Republican, said he would urge his colleagues to pass a Senate bill that features more comprehensive sanctions.

“It’s a first step and an important one,” he said of Wednesday’s action. “I want to go further and target the assets of some of these individuals.”

“Virtually every top-level official in the Venezuelan government is stealing money,” he said, during a roundtable discussion with reporters. “Corruption — skimming off the top — is widespread throughout the Venezuelan government.” And a lot of that money is being invested in the U.S., he added.

The bill, which Rubio co-sponsored, is similar to a version that passed the House in May and also includes the targeted freezing of assets.

While the State Department won’t say who might be snared by Wednesday’s measures, Rubio said “my understanding is it will be a number of the people we’ve identified publicly in the past.” In May, Rubio released a list of 23 Venezuelan officials he said should be targeted.

The announcement comes just days after a diplomatic tug-of-war over Venezuelan Gen. Hugo Carvajal who is wanted in the United States on drug charges. The former head of Venezuela’s military intelligence, Carvajal was detained in Aruba last week for four days at the request of the United States. However, the island nation and the Kingdom of the Netherlands were strong-armed by Venezuela to send him home, rather than wait for a U.S. extradition request, the State Department and others said.

Venezuela claims Carvajal is innocent and detained as part of a U.S.-backed destabilization campaign.

“In the aftermath of the Venezuelan regime pulling out all the stops to protect and give a safe haven to a notorious narco-trafficker, it’s disappointing that the Obama administration has yet to implement strong sanctions against the Maduro regime,” U.S. Rep. Ileana Ros-Lehtinen, R-Miami, who sponsored the House sanctions bill, said in a statement. “Not only should we deny visas to Maduro’s cronies but we should also expand those visa restrictions to immediate family members of human rights violators and freeze their assets and property in the U.S.”

Other South Florida politicians also weighed in. U.S. Rep. Joe Garcia, a Democrat from Miami and a co-sponsor of the House bill, talked about officials who “spend weekends vacationing in Miami living the lavish lifestyle they denounce back home.”

U.S. Rep. Mario Diaz-Balart, a Republican from Miami and also a co-sponsor of the bill, built on those comments, calling the action “a weak slap on the wrist.”

“These weak actions today will do little to change the regime’s affinity for attacking peaceful civilians, launching bogus criminal charges on pro-democracy opposition leaders, and using live ammunition and torture of arrested protesters,” he said.

But some worry that even mild sanctions could create a backlash.

A poll by the Venezuelan research firm Datanalisis in May showed that 73 percent of Venezuelans disagreed with sanctions.

Maduro often accuses the United States of working with the Venezuelan opposition to try to topple his socialist administration and sanctions play into that narrative.

“In political terms, it’s not all that constructive or timely,” said David Smilde, a senior fellow at the Washington Office on Latin America. “It will give Maduro the chance to deflect criticism and portray this as a battle between Venezuela and the United States.”

The move might also undermine any regional efforts to press for reforms, he said.

Until Wednesday, the White House and State Department had also argued that sanctions might strengthen Maduro’s hand.

José Miguel Vivanco with Human Rights Watch said he thought external pressure was needed to get the Venezuelan government to improve its human rights record. But Vivanco, who helped prepare the group’s recent report “Punished for Protesting,” worried that there was a possibility they might backfire.

“Unfortunately, there’s a real risk that unilateral sanctions by the U.S. could be counterproductive,” he said, “especially if the administration doesn’t provide a clear and compelling explanation of what individuals are being targeted and what exactly they’ve done to deserve this.”

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